Allah says:

فَنَجَّيْنَاهُ وَأَهْلَهُ أَجْمَعِينَ ﴿١٧٠﴾

إِلَّا عَجُوزًا فِي الْغَابِرِينَ ﴿١٧١﴾

So, We saved him and his family, all. Except an old woman among those who remained behind.

This was his wife, who was a bad old woman. She stayed behind and was destroyed with whoever else was left.

This is similar to what Allah says about them in Surah Al-A`raf and Surah Hud, and in Surah Al-Hijr, where Allah commanded him to take his family at night, except for his wife, and not to turn around when they heard the Sayhah as it came upon his people. So they patiently obeyed the command of Allah and persevered, and Allah sent upon the people a punishment which struck them all, and rained upon them stones of baked clay, piled up.